Connection between stability tests of Middleton/Goodwin and Lev-Ari/Bistritz/Kailath

Here it is shown that two seemingly unrelated stability tests, the Lev-Ari/Bistritz/Kailath test for systems in the discrete-time shift-operator formulation and the test proposed by Middleton and Goodwin for systems in the discrete-time delta-operator formulation, are closely related. It is shown that they both belong to a family of stability tests spanning from the discrete-time to the continuous-time, including the well-known Routh test.